equation of the perpendicular bisector of the line segment joining (5,7),(3,1) is
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B = (3,1)
midpoint of A and B
= ( 5+3/2 , 7+1/2)
= (8/2 , 8/2)
= (4,4)
slope of AB = (1-7)/(3-5) =-6/-2 = 3
slope of the perpendicular = -1/3
the perpendicular passes through (4,4)
the equation ,
y - 4 = -1/3 (x-4)
3y - 12 = -x + 4
3y + x = 16